I am definitely not the right person to give you a source on this. The only thing I would argue is that there is enough in common between all human languages that they can all be implemented and processed using the same basic machinery, i.e. the brain. There are lots of interesting discussion points from your question. It makes me think about how a universal translation system would have to work. If it were possible, it would have to be this overarching model of models, so to speak, that fully encompassed all the rules of all known languages. Would this model of models still be a single model? I think so, as long as it could be described or generated using finite memory. This becomes particularly nuts when you consider OP's point that perception has to be considered, but theoretically I think it's possible.

I completely agree with everything you're saying here. It's a bit late for me to really get into it, but I will come back to the discussion. What you're saying here reminds me of the notion of 'concepts' (I think) that I've heard cognitive scientists talk a lot about recently. That these notions are really fuzzy, and completely designed and influenced by all sorts of context.

When I say logical framework, I suppose I mean a formal system of logic with an axiomatization and calculus. I'm really just being nitpicky - the assertion that something cannot possibly exist is a much more difficult thing to prove.

I think my point is that even those complex things like context and perception might be possible to formalize, more or less, even if it requires some inconsistency or stochasticity. I think what we can probably agree on is that it's relatively easy to demonstrate that a given system of logic, such as propositional or first order logic, cannot possibly account for all the rules of human language - that's exactly what is discussed in the article, and by no means do I mean that in a way to diminish the effort - this is a really important discussion for mathematicians and cognitive scientists to have.

Finally, absolutely. I completely agree that a probabilistic or stochastic model is completely necessary to lay out the 'rules' of human language. I guess I'm just coming from the perspective of "There's got to be a way we can model this, more or less, using classical computational mechanisms." It's definitely not propositional or first order logic, as you laid out, but it could still be symbolic, even if it requires something silly sounding like infinitely many rules in the grammar.

I'd be curious to know your thoughts on artificial models for natural language, or artificial intelligence. If you've written anything on the subject I'd be happy to read it.

Great! To be clear, I liked the article, and I agree with most of the points as they relate to propositional or first order logic. To me, though, the title is a bit sensational. I'm a mathematician and computer scientist (PhD candidate, so don't take me too seriously!), and a lot of my work has been in formal languages and complexity theory. I interpret the title as meaning "There exists no logical framework in which the syntax and semantics of human language can be fully expressed." While I agree that such a system has not yet been identified, I think that there has been no mathematical proof to support the claim. And it's not for lack of trying. I might be too quickly jumping to a related idea, but if I understand the conjecture, it reminds me very much of Roger Penrose's proof that human intelligence cannot possibly be explained or implemented using a Turing machine, the classical mathematical formalization of a classical computer. The proof, in my opinion and in that of many others, is not well founded and I think most critics think that he's probably wrong, at least in his certitude.

Relating it to this article, I think we're sometimes too quick to attribute human intelligence or some of its aspects like natural language to processes that cannot be modeled either symbolically, like in the case of logic, or computationally, like in the case of things like artificial neural networks and other mathematical models. With respect to logic, I suggest that there could very well be a logical framework capable of fully encompassing human language - but it certainly will not be one as simple as propositional or first order logic. But there is so much more than that. The rules of human language must lie somewhere in the realm of an inconsistent logical system or one that is incomplete. I'll leave it to people better versed than me in fundamental maths to lay out the relationship between Godel's incompleteness theorem and natural language - but Godel, Escher, Bach - a seminal book on the subject is a great place to start. In short though, I would argue that there is no complete and consistent logical system in which human language can be fully explained, and I think the article does a good job at laying out the intuitions behind the argument. Another possibility is a very large, but still finitely axiomatized system in which exceptions really are the rule.

In a more complex logical system, where necessarily the logic is either incomplete or inconsistent, there could very well be an axiomatization of human language that ticks all the right boxes. I don't assert that I can produce such a system, but to say that it doesn't or can not possibly exist requires a more detailed discussion and proof.

On a final note, I'd just like to bring up an idea. I think that just because we cannot explain the emergent behaviour of a large system using one formal system or the other, doesn't imply that the underlying computations are not simple. We observe this in biological and artificial neural networks. So even if there is no simple logic that can explain human language, it could still be the case that the individual neurons in our brains really are that simple, and that it is due to the complexity of their interconnectedness that such amazing processes emerge.

I would also just point out that logic can be in reference to one of may different systems, some of which may be powerful enough to model natural language. Would be happy to provide some more points if people are interested!

Especially considering your strat has HSS, getting a guitar with a single coil in the bridge is going to be super useful and very different from what you've got now. And for my money tele's play and sound drastically different from strats, even if they both have single coils. I was reluctant for the longest time (I have a great MIM strat that's my main guitar for covers, too) but when I finally got just a Squier Classic Vibe tele, it instantly became my favourite guitar to randomly pick up at home. And to me, tele's need to be played a little differently from other guitars, so you might find it to be a nice challenge, too! Good luck!